The marital friends party

[Exploited]

We was having a big party. Only martial couples (wife + husband) was invited (there were NO single guests). Total of 60 martial couples attended to the party (that was a huge party indeed!). Of course I was a part of a martial couple too - I was with my wife there.

At the start of the party all guests was shaking hands between each other (of course a husband will not shake hands with his own wife - they shake hands with other married couple!).

At the end of the party I made a quick survey. I asked everybody "With how many people you shaked hands today?"... Amazingly, but every guest gave me different answer - it came that there was no two people who shaked hands with other guests the same times (for example if guest X shaked hands 23 times today - then no other guest Y shaked hands the same 23 times)! What a co-incidence... nevermind - lets go to my question for you:
How many times my wife shaked hands with guests on the party?

[keaglez]

Zero??

[Exploited]

it is not zero, but how did you calculated that number?

[keaglez]

LOL, i guess if there are 120 people (60 couple), and every of them are not shaked hand with his/her wife/husband so the maximum is one people can shake 119 people hand.. Well, there are 120 people and no one same, so 119 people will shake 1 until 119 hand... So the 0 is the last possibilities for the 120th people...

[Exploited]

Let's start from the situation with 4 people:

me   wife
    \  |
M1   F1

Check it out and you will see that it is the only solution:
M1 - shaked hands 0 times
My Wife - shaked hands 1 time
F1 - shaked hands 2 times
=> all guests shaked hands different amount of times & no man shaked hands with his wife

This is the only possible solution (try it out)...

However I will leave you with the two couples example... now it's your turn to give me the answer for N=60 ))

[BlinK_]

I think its 118.

She shook hands with everybody except herself and exp.

[keaglez]

LOL, i forgot that...

[Exploited]

Blink_ not true...

Try to extend the problem with 2,3,4 couples and then make it for N couples recursively

[Exploited]

ok it's hard to represent it in text mode, but it happens that if you add one man and woman additional - your wife will shake hands one more time

=> if we have 1 couple she shake hands 1 time, 2 couples - 2 times, "n" couples - "n" times => my wife shaked hands 60 times total